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SCIENTIFIC NOTATION: Abbreviating numbers

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What is an EXPONENT? A SUPERSCRIPT after “x 10” or “E”SUPER Ex: “x 10 5” or “E5” Denotes how many powers of ten 10 5 = 10 x 10 x 10 x 10 x 10 Answer is a 1 followed by zeros (defined by the exponent) 100,000

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BIG NUMBERS Positive Exponents 5,987,774,231,541

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Numbers smaller than 1 Negative Exponents 0.0000076319

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MOVE THE DECIMAL TO THE RIGHT Moving the decimal (+)

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MOVE THE DECIMAL TO THE LEFT Moving the Decimal (-)

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PRACTICE: 1. 4.67 x 10 5 2. 1.94 x 10 1 3. 7.69 x 10 0 4. 2.48 x 10 -2 5. 7.35 x 10 -6 6. 2.52 E -4 = 467000 = 19.4 = 7.69 = 0.0248 = 0.00000735 = 0.000252

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Converting to Scientific Notation 1.FIND THE DECIMAL 2.MOVE THE DECIMAL SO THE BASE NUMBER IS LESS THAN 10, GREATER THAN 1 BASE NUMBER 3.COUNT THE NUMBER OF JUMPS

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4. ROUND ANSWERS SO THEY HAVE THREE (3) DIGITS STARTING FROM THE LEFT 5. ADD “ X 10” (or E) 6. THE NUMBER OF JUMPS IS YOUR EXPONENT! Cont.

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PRACTICE: 1. 56420 2. 123 3. 718134 4. 6132 = 5.64 x 10 4 = 1.23 x 10 2 = 7.18 x 10 5 = 6.13 x 10 3

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NEGATIVE EXPONENTS If your number is less than 1 you will have a negative exponent!

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PRACTICE: 1. 0.0184 2. 0.000567 3. 0.06 0.06 4. 0.00057912347 = 1.84 x10 -2 = 5.67 x10 -4 = 6.00 x10 -2 = 5.79 x10 -4

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Three Number Rule o If there are not enough numbers add zeros o If there are too many numbers round

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Rounding START FROM THE LEFT AND COUNT THE FIRST 3 NUMBERS IF THE FOURTH NUMBER IS A 5 OR ABOVE ROUND UP! DROP UNNECESSARY NUMBERS

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PRACTICE: Put the problem in Sci. Not. 1 st :Round 1. 23794 2. 0.0001146 3. 468992 4. 0.9999 5. 2100100 6. 0.000002 =2.38 x 10 4 =1.15 x 10 -4 =4.69 x 10 5 =1.00 x 10 0 =2.10 x 10 6 =2.00 x 10 -6

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SCIENTIFIC NOTATION PRACTICE Convert the following to normal notation: 1. 5.23 x 10 3 2. 2.90 x 10 -9 3. 4.18 x 10 -5 4. 2.71 E7 Convert the following to SCIENTIFIC notation (ROUND TO 3 DIGITS): 1. 0.00854 2. 349001 3. 0.03 4. 1238 Round to 3 DIGITS (you have to put them in sci. not. first!) 6349 0.3487 7956143278 0.0000000000000799

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Prefixes: Super- Above Ex: X 2 Sub- Below Ex: X 2

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Exponent Rule! DECIMAL MOVES EXPONENT becomes MORE POSITIVE (+1) DECIMAL MOVES EXPONENT becomes MORE NEGATIVE (-1) 0.214 x 10 -2 2.14 x 10 -2 2.14 x 10 -3

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Aim: How can we express a large or small number?

Aim: How can we express a large or small number?

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